Notes on GIT and symplectic reduction for bundles and varieties

Details Notes on GIT and symplectic reduction for bundles and varieties Notes on GIT and symplectic reduction for bundles and varieties

2005-12-17

arxiv.org/abs/math/0512411v3

Surveys in Differential Geometry, 10 (2006): A Tribute to Professor S.-S. Chern.

Mathematics

Algebraic Geometry

Expanded version of talk at JDG 2005 conference, for "Surveys in Differential Geometry". 51 pages, 15 figures. Final version

Scientific paper

These notes give an introduction to Geometric Invariant Theory and symplectic reduction, with lots of pictures and simple examples. We describe their applications to moduli of bundles and varieties, and their infinite dimensional analogues in gauge theory and the theory of special metrics on algebraic varieties. Donaldson's "quantisation" link between the infinite and finite dimensional situations is described, as are surprisingly strong connections between the bundle and variety cases.

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